Numerical integration of an ODE?

Hey! I'm trying to integrate the following 2nd order ODE:

from time t=0 to any random time, say t=50 seconds

ω and A are constants.

I need to integrate the above equation twice, numerically. Any idea how i can do this and what method i'll be using?

thanks

[John D'Errico]

Read the help for ODE45. You will find examples in there.

doc ode45

[riccardo]

Why numerically ?

If A and w are constants, x(t) = A*sin(w*t) is surely the primitive (plus initial conditions if not zero).

Answer 1

[Priyanka Rai]

To be able to integrate 2nd Order ODE numerically you can use the following methods, based on your use case:

1. If function f is to be integrated, then for definite integral you can use

int(f, a, b)

Refer this link : https://www.mathworks.com/help/symbolic/integration.html#:~:text=Integration%20%20%20%20Mathematical%20Operation%20%20,%281%2C%20z%29%29%20or%20int%20%28besselj%20%281%2C%20...%20

2. Numerically evaluate double integral

q = integral2(fun,xmin,xmax,ymin,ymax)

approximates the integral of the function z = fun(x,y) over the planar region xmin ≤ x ≤ xmax and ymin(x) ≤ y ≤ ymax(x).

Refer this link : https://www.mathworks.com/help/matlab/ref/integral2.html

Numerical integration functions can approximate the value of an integral whether or not the functional expression is known.When you know how to evaluate the function, you can use integral to calculate integrals with specified bounds.

You can refer to this blog for more information as well: https://blogs.mathworks.com/loren/2014/02/12/double-integra tion-in-matlab-methods-and-handling-discontinuities-singularities-and-more/